Hess's law looks intimidating until you realize what it actually asks of you: rearrange a few given reactions until they add up to the target reaction, then add their enthalpies. No new chemistry, just careful bookkeeping. This Hess's law walkthrough lays out the three moves you are allowed to make, then runs through a worked example end to end so the rules stick.
Why Hess's Law Works
Enthalpy is a state function. That means ΔH depends only on the starting and ending states of the system, not the route between them. Whether a reaction happens in one explosive step or three slow ones, the total enthalpy change is the same — as long as the reactants and products are the same.
That single fact is Hess's law in disguise. If you can break the target reaction into steps whose ΔH values you know, you can just add those ΔH values to get the target ΔH. You never have to run the reaction in the lab. You only have to find a path on paper.
The Three Moves You Are Allowed
When you stitch known reactions together to build the target reaction, three operations are legal — and each one changes ΔH in a predictable way.
- Reverse a reaction. Flip reactants and products, and the sign of ΔH flips with them. If A → B has ΔH = −100 kJ, then B → A has ΔH = +100 kJ. Reversing means the system now climbs the energy hill it once descended.
- Multiply a reaction by a coefficient. Double all the coefficients and you double ΔH. Multiply by ½ and you halve it. ΔH is reported per mole of the reaction as written, so it scales linearly with the equation.
- Add reactions together. Stack the equations as if they were numerical equalities. Anything that appears on both sides — same compound, same phase, same amount — cancels. Add the ΔH values for the same total.
That is it. Reverse, scale, add, and cancel. Every Hess's law problem is some combination of those four motions.
A Worked Example: ΔH for the Combustion of Carbon to CO
Find ΔH for C(s) + ½ O₂(g) → CO(g).
The reaction is hard to run cleanly in a lab — burning carbon gives a stubborn mix of CO and CO₂ — so you build it from two reactions whose ΔH values are tabulated.
- Reaction 1: C(s) + O₂(g) → CO₂(g) ΔH₁ = −393.5 kJ
- Reaction 2: CO(g) + ½ O₂(g) → CO₂(g) ΔH₂ = −283.0 kJ
Step 1: Match the target's left and right sides
The target needs C(s) on the left, CO(g) on the right, and the net to involve ½ O₂(g). Reaction 1 already has C(s) on the left, so leave it alone. Reaction 2 has CO(g) on the left, but the target wants CO(g) on the right — so reverse Reaction 2.
Reversing Reaction 2 flips its sign:
- Reaction 2 reversed: CO₂(g) → CO(g) + ½ O₂(g) ΔH = +283.0 kJ
Step 2: Add and cancel
Stack them and combine:
Reaction 1: C(s) + O₂(g) → CO₂(g)
Reaction 2 reversed: CO₂(g) → CO(g) + ½ O₂(g)
Sum: C(s) + O₂(g) + CO₂(g) → CO₂(g) + CO(g) + ½ O₂(g)
CO₂(g) appears on both sides — cancel. O₂(g) appears as 1 mol on the left and ½ mol on the right — subtract to leave ½ O₂(g) on the left. The result is:
C(s) + ½ O₂(g) → CO(g) — exactly the target.
Step 3: Add the enthalpies
ΔH(target) = ΔH₁ + ΔH(Reaction 2 reversed) = (−393.5) + (+283.0) = −110.5 kJ.
That is the standard enthalpy of formation of carbon monoxide, ΔH°f. Two table values, one sign flip, one addition.
A Note on Scaling: When Coefficients Do Not Match
Many problems hand you reactions with coefficients that do not match the target. You scale before adding. Suppose a reaction in the table makes 2 mol of product but the target needs 1 mol — multiply that reaction by ½ and multiply its ΔH by ½ as well. The two moves stay locked together: whatever you do to the equation, do to the enthalpy. If after adding you still see a fractional coefficient that should be a whole number, multiply the whole sum through to clear it, and multiply ΔH the same way.
Common Mistakes That Cost Points
The math itself is light. The errors are almost always bookkeeping.
- Forgetting to flip the sign when you reverse a reaction. Reversing without flipping is the most common mistake on Hess's law problems. Write the new ΔH next to the reversed equation immediately, before you lose track.
- Cancelling species in different phases. H₂O(l) and H₂O(g) are not the same — they have different enthalpies. Only cancel a species when its formula and phase match exactly on both sides.
- Scaling the equation but not ΔH. Whenever you multiply a reaction by a coefficient, multiply its ΔH by the same coefficient. Many students update the equation and leave the original ΔH untouched.
Getting Help
Hess's law builds on the enthalpy basics — exothermic versus endothermic and what ΔH stands for. If those signs feel unclear, start there. For the full set of foundational walkthroughs, browse the General Chemistry study guides.
Conclusion
A Hess's law walkthrough is bookkeeping, not new chemistry. Take the target reaction. Pick a set of known reactions that share its species. Reverse them, scale them, and stack them until the cancellations leave exactly the target, then add the ΔH values along the way. Reverse flips the sign, scaling multiplies ΔH by the same factor, and only identical species — same formula, same phase — cancel. Practice on three or four examples and the moves become automatic.
